EU negotiators believe a trade deal will have to follow a Brexit deal - which could cause a bust-up over the negotiation timeline.
Officials think Britain should lay out its exit before discussing its future links with current member states.
- ITV News Political Correspondent Carl Dinnen reports from Brussels
The family of Aysha Frade, the woman who was killed in the Westminster attack, has paid tribute to her, one week on from the tragedy which left three other innocent victims dead.
In a statement issued by the Metropolitan Police, the family said: "Our beloved Aysha; caring daughter, loving sister, amazing wife, irreplaceable aunt, thoughtful, supportive friend and the best and coolest of mummies.
"You were ripped away from our lives in the cruellest and most cowardly of ways. We now pray that you guide and protect not only us, but all of London, from further evil.
"You will always be remembered as our guardian angel who never shied away from facing up to bullies.
"There are no words to even begin to describe the crushing pain and eternal void left in our hearts."
Nigel Farage has celebrated the triggering of Article 50 by going to the pub for a pint.
The former UKIP leader said it was a "big day" and he was having a "minor celebration".
He added: "Every day is a sad day in the European Union because every single day that goes by opposition to the project grows amongst all 28 member states.
"The European Union may have been a good idea 60 years ago. It doesn't work anymore."
The chief Brexit representative for the European Parliament has said that the basic principle driving Britain and the EU's new relationship should be to put "citizens first".
European negotiator Guy Verhofstad told a news conference the parliament was "completely against citizens becoming bargaining chips in negotiations."
"When we talk about citizens, it's citizens in Britain and citizens in the European Union," he said. "It's an absolute priority that the rights of these citizens is settled."
Verhofstad said that the EU and Britain should agree on a general framework of a new relationship withing two years. Britain can change its mind on leaving the EU - if all other EU states agreed to its return, he added.